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If \(f(x)=x^2\), \(g(x)=x\), and \(h(x)=1\), what is the value of \((f+2g+h)(x)\)?यदि \(f(x)=x^2\), \(g(x)=x\) और \(h(x)=1\) हों, तो \((f+2g+h)(x)\) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \((x+1)^2\)\((x+1)^2\)
Function addition is performed pointwise: \((f+2g+h)(x)=f(x)+2g(x)+h(x)=x^2+2x+1=(x+1)^2\). Option B omits the coefficient 2 of \(g(x)\). Exam tip: In a linear combination, multiply each function by its stated coefficient before adding.फलनों का योग बिंदुवार किया जाता है: \((f+2g+h)(x)=f(x)+2g(x)+h(x)=x^2+2x+1=(x+1)^2\)। विकल्प B में \(g(x)\) के साथ गुणांक 2 नहीं लगाया गया है। परीक्षा-युक्ति: किसी रैखिक संयोजन में प्रत्येक फलन के सामने दिए गए गुणांक को अवश्य शामिल करें।
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